Early voting is a very simple process really, in its simplest form you vote a day early in designated early voting stations. Its purpose is also very simple, relieve crowding in voting stations on the election day, and thus increase participation. It's a practice that, in one form or another, is followed in several countries. In the US early voting is regulated at the state level, and not all states offered early voting in the 2012 election1.
As for the controversy, it was build around the opinion that the practice would eventually favour the Democrats as groups that were more likely to to vote for them also tended to not show up on election day (for one reason or another). Some states offered early voting via mail, which clearly is more convenient for a lot of people:
Another voter, Myrna Levey of Cleveland, Ohio, said she voted early for Obama, by mail through an absentee ballot.
"It's more convenient," said Levey, 74. "They moved our voting place several blocks away and it is no longer in walking distance."
Another part of the controversy was that the Democrats push for early voting, exemplified by Barack Obama's early vote, was mainly to counter-act a wave of recent changes in US voting laws, some (if not most) backed by Republicans, that introduced a number of restrictions, such as the voter ID laws. It has been argued that these changes were unfavourable for groups of people that traditionally voted for the Democrats:
These new restrictions fall most heavily on young, minority, and low-income voters, as well as on voters with disabilities. This wave of changes may sharply tilt the political terrain for the 2012 election. Based on the Brennan Center’s analysis of the 19 laws and two executive actions that passed in 14 states, it is clear that:
- These new laws could make it significantly harder for more than five million eligible voters to cast ballots in 2012.
- The states that have already cut back on voting rights will provide 171 electoral votes in 2012 – 63 percent of the 270 needed to win the presidency.
- Of the 12 likely battleground states, as assessed by an August Los Angeles Times analysis of Gallup polling, five have already cut back on voting rights (and may pass additional restrictive legislation), and two more are currently considering new restrictions.
From what I gathered the main arguments against early voting were:
- It allows otherwise inactive / uninterested voters to vote,
- Some states allowed people to vote weeks before election day, and those who took advantage of that voted without having all the information,
- The integrity of the ballot was questioned, especially for the states that allowed absentee voting via mail, and
- It wasn't worth the extra cost as studies have shown that it doesn't significantly increase participation (and it might even depress it).
In my very humble opinion all the arguments, pro and con, are politically biased and the actual significance (if any) of early voting in the 2012 election is very much a matter of debate:
The blizzard of numbers, of claims and counterclaims, can be so daunting it's tempting to just throw up your hands and decide there's no truth to be had, just spin. But an objective analysis of early turnout can provide valuable tea leaves for Election Day. In many states, election officials disclose how many Democrats and Republicans have voted thus far. We don't know who they're voting for, but in most states, this alignment is a good proxy for the candidates. (Then there's the mystery of those voters who aren't affiliated with a party. In polls, independent voters have generally favored Romney, leading his campaign to claim an edge in this category, but for the purposes of analyzing early voting it's impossible to tell.) It's important to consider which party has historically had the early vote advantage -- Democrats, in most states -- and whether early voting makes up a substantial amount of the vote, which varies from state to state.
...
This analysis isn't conclusive; it's a faint clue at best. But with as much as 40 percent of the nationwide vote likely to have been cast before the polls open on Tuesday, here's what the early vote is telling us so far.
1 See: Early Voting Rules for a thorough breakdown of how each state handled early voting.